Combine Cycles passes in way compatible with photoshop
According to this, Linear Dodge is the same as Add in Blender. However, if you are working with 8 or 16bit jpg/png/tga, Photoshop by default will works in display-referred space (i.e. everything is gamma corrected and non-linear), so the results of adding multiple render layers together in a non-linear space will be WRONG.

The only way to work in a linear space, which is absolutely critical, is to use 32bit EXR, that's the only way Photoshop will operate in linear space, and follow this workaround.

In short, don't use Photoshop. It's really not designed for linear values and will give you wrong results  unless you specifically configure it to work in linear space.